Value of Log 1 to 10: Logarithmic Functions & Its Types

Content Curator

Logarithm is the most convenient technique to express huge numbers in mathematics. Logarithm is defined as the power to which any integer must be raised to get some values. Exponentiation is also known as the inverse process of logarithms.

Read Also: Value of Log 0

Table of Content

Types of Logarithmic Functions
Logarithmic Rules
Value of Log 1 to 10 for Log Base 10
Value of Log 1 to 10 for Log Base e
Things to Remember
Previous Year Questions
Sample Questions

Keyterms: Log, Logarithm, Exponential functions, Integer, Base, Logarithm functions, Natural logarithmic functions, Common logarithmic functions

Types of Logarithmic Functions

[Click Here for Sample Questions]

Logarithm is a quantity that represents the power with which a fixed number's base is raised to generate a given number. The logarithmic function's general representation is

f(x) = log_a x

The two types of logarithmic functions are, in general,

The base of a common logarithmic function is 10. This function is represented by log₁₀ or log.
The base of the natural logarithmic function is e. This function is represented by the letters ln or log_e.

Also Read:

Related Articles
Sequence and Series	Arithmetic Progression	Geometric Progression
Geometric Mean	Straight Lines	Angle Between Two Lines

Logarithmic Rules

[Click Here for Previous Year Questions]

Quotient rule- The quotient rule involves dividing two numbers by the same base and then subtracting the exponents.

Log_b M/N = Log_b M - Log_b N

Product Rule- The product rule involves multiplying two numbers with the same base and then adding the exponents.

Log_b MN = Log_b M + Log_b N

Power Rule- Exponents' expressions are raised to power in the power rule, and then the exponents are multiplied.

Log_b M_p = P log_b M

Value of Log 1 to 10 for Log Base 10

[Click Here for Sample Questions]

Here is a list of the values of log 1 to 10 (common logarithm- log₁₀ x).

Common Logarithm to a Number (log₁₀ x)	Log Value
Log 1	0
Log 2	0.3010
Log 3	0.4771
Log 4	0.6020
Log 5	0.6989
Log 6	0.7781
Log 7	0.8450
Log 8	0.9030
Log 9	0.9542
Log 10	1

Also Read:

Related Articles
Real-Valued Function	Trigonometric Functions	Complex numbers and Quadratic Equations
Hyperbola	Ellipse	Parabola

Value of Log 1 to 10 for Log Base e

[Click Here for Previous Year Questions]

This table shows the value of log 1 to 10 in terms of the natural logarithm (log_e x).

Natural Logarithm to a Number (log_e x)	Ln Value
ln (1)	0
ln (2)	0.693147
ln (3)	1.098612
ln (4)	1.386294
ln (5)	1.609438
ln (6)	1.791759
ln (7)	1.94591
ln (8)	2.079442
ln (9)	2.197225
ln (10)	2.302585

Things to Remember

In the 2nd century BC, India was the first country to apply logarithm.
Michael Stifel, a German mathematician, was the first to employ the logarithm in contemporary times.
The main benefit of utilizing base 10 logarithms is that they are simple to calculate mentally for some particular numbers. For example, the log base 10 of 1.000,000 is 6, and all you have to do is count the zeros.
For theoretical work, natural logs are more convenient. They're simple to figure out quantitatively.
Exponentiation is also known as the inverse process of logarithms.

Read Here: Value of Log 1

Previous Year Questions

The differential coefficient of f (Sinx) w.r.t. x where f(x)=logx is….[KCET 2004]
The differential coefficient of log10x with respect to logx10 is….….[KCET 2016]
If log72=?, then the value of log49(28) is….
The derivative of y = xsinx is...[UPSEE 2016]
The derivative of (logx)x with respect to log x is….
The sum of the divisors of 2⁴⋅3³⋅5³ is…..
The value of =dxd[xnlogaxex]=…
The value of dxd[xnlogaxex] is...[JKCET 2013]
If a=log23,b=log25,c=log72, then log14063 in terms of a, b, ca,b,c is…...[BITSAT 2007]
The general value of the real angle θ, which satisfies the equation,...[WBJEE 2019]

Sample Questions

Ques: Name two different types of logarithmic functions. (2 marks)

Ans: The two types of logarithmic functions are:

The base of a common logarithmic function is 10. This function is represented by log₁₀ or log.
The base of the natural logarithmic function is e. This function is represented by the letters ln or log_e.

Ques: Calculate the difference between log1 and log0. (2 marks)

Ans: log1 – log 0 (Given)

Value of Log 1 = 0 and Value of log 0 = - ∞

Hence, log 1+ log 0 = 0-(-∞) = ∞

Ques: What is the value of log264? (3 marks)

Ans: Using the base formula,

Log₂ x = log₁₀ x/ log₁₀ 2

= log₂ 64 = log₁₀ 64/ log₁₀ 2

=1.806180/ 0.301030

= 6

Ques: What are some of the applications of a logarithm? (3 marks)

Ans: John Napier was the first to introduce the concept of the logarithm. Many scientists, navigators, engineers, and others afterward used it to make various calculations quickly. The logarithm notion is also commonly employed in the fields of science and technology.

Problems based on logarithm can be simply calculated with the logarithm calculator. In surveying and celestial navigation, the logarithm is also utilized. The logarithm is also employed in computations such as determining the soundness of a building, the intensity of an earthquake on the Richter scale, and the acidity of radioactivity (pH =- log 10 H⁺, etc.).

As a result, the logarithm is quite significant in today's world.

Ques: Describe product rule. (2 marks)

Ans: Power rule- Exponents' expressions are raised to power in the power rule, and then the exponents are multiplied.

Log_b M_p = P log_b M

Ques: What is the value of Log₁₀ 0? (1 mark)

Ans: Log₁₀ 0 = Not Defined

Also check:

Class 11 & 12 PCMB Study Guides
NCERT Solutions for Class 11 Biology	Comparison Topics in Biology	Biology Study Notes
Biology MCQs	Class 11 Notes	NCERT Class 11 Biology Book
Physics Study Notes	Class 12 Physics Book PDF	Class 12 Physics Practicals
Important Derivations in Physics	SI units in Physics	Important Physics Constants and Units
Class 12 Physics Syllabus	NCERT Solutions for Class 12 Chemistry	NCERT Solutions for Class 12 Biology
NCERT Solutions for Class 12 English	NCERT Solutions for Class 12 Maths	Class 12 Chemistry Practicals
Class 12 Chemistry Notes	Class 12 Biology Notes	Class 12 Maths Notes
Class 12 PCMB Notes	NCERT Class 12 Biology Book	NCERT Class 12 Maths Book
NCERT Class 12 Textbooks	NCERT Solutions for Class 11 Maths	NCERT Solutions for Class 11 Physics
NCERT Solutions for Class 11 Chemistry	NCERT Solutions for Class 12 Physics	NCERT Solutions for Class 11 English
NCERT Class 11 Chemistry Book	NCERT Class 11 Physics Book	Topics with relation in physics
Choice based questions in physics	Important Maths Formulas	Important Chemistry Formulas
Class 11 PCMB Syllabus	Chemistry Study Notes	Formulas in Physics
Periodic Table in Chemistry	Important Chemical Reactions	Comparison topics in Chemistry
Comparison Topics in Maths	Class 12 Physics Notes	Important Named Reactions
Maths MCQs	Topics for Comparison in Physics	Chemistry MCQs

CBSE CLASS XII Related Questions

1.
Find:

The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:
- \(-\frac{\pi}{2}\)
- \(-\frac{\pi}{4}\)
- \(\frac{\pi}{4}\)
- \(\frac{\pi}{2}\)
View Solution
2.
A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.
3.
Differentiate \( \tan^{-1}\left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) \) with respect to \( \cos^{-1}(x^2) \).
View Solution
4.
Find:
Let \(A=[a_{ij}]\) be a \(2\times2\) matrix whose elements are given by \[ a_{ij}=\frac{(2i-j)^2}{3} \] Find the transpose matrix \(A'\).
- \(\begin{bmatrix} \frac{1}{3} & 3 \\ 0 & \frac{4}{3} \end{bmatrix}\)
- \(\begin{bmatrix} \frac{1}{3} & 0 \\ 3 & \frac{4}{3} \end{bmatrix}\)
- \(\begin{bmatrix} \frac{4}{3} & 3 \\ 1 & 0 \end{bmatrix}\)
- \(\begin{bmatrix} \frac{4}{3} & 0 1 & \frac{3}{3} \end{bmatrix}\)
View Solution
5.
Find: \[ \int \frac{x^2}{(x^2-1)(x^2+4)}\,dx \]
View Solution
6.
If \( xy = e^{x - y} \), then find \( \frac{dy}{dx} \).
View Solution